diff --git a/migrations/capcons/capabilitymigration.go b/migrations/capcons/capabilitymigration.go
index 763003d8c6..a37fd234e7 100644
--- a/migrations/capcons/capabilitymigration.go
+++ b/migrations/capcons/capabilitymigration.go
@@ -41,7 +41,7 @@ type CapabilityMigrationReporter interface {
 // CapabilityValueMigration migrates all path capabilities to ID capabilities,
 // using the path to ID capability controller mapping generated by LinkValueMigration.
 type CapabilityValueMigration struct {
-	CapabilityIDs map[interpreter.AddressPath]interpreter.UInt64Value
+	CapabilityIDs *CapabilityIDMapping
 	Reporter      CapabilityMigrationReporter
 }
 
@@ -75,7 +75,7 @@ func (m *CapabilityValueMigration) Migrate(
 		oldCapability := value
 
 		capabilityAddressPath := oldCapability.AddressPath()
-		capabilityID, ok := m.CapabilityIDs[capabilityAddressPath]
+		capabilityID, ok := m.CapabilityIDs.Get(capabilityAddressPath)
 		if !ok {
 			if reporter != nil {
 				reporter.MissingCapabilityID(
diff --git a/migrations/capcons/linkmigration.go b/migrations/capcons/linkmigration.go
index 1d7f1697f5..c26744585d 100644
--- a/migrations/capcons/linkmigration.go
+++ b/migrations/capcons/linkmigration.go
@@ -40,7 +40,7 @@ type LinkMigrationReporter interface {
 
 // LinkValueMigration migrates all links to capability controllers.
 type LinkValueMigration struct {
-	CapabilityIDs      map[interpreter.AddressPath]interpreter.UInt64Value
+	CapabilityIDs      *CapabilityIDMapping
 	AccountIDGenerator stdlib.AccountIDGenerator
 	Reporter           LinkMigrationReporter
 }
@@ -182,8 +182,7 @@ func (m *LinkValueMigration) Migrate(
 	// Record new capability ID in source path mapping.
 	// The mapping is used later for migrating path capabilities to ID capabilities,
 	// see CapabilityMigration.
-
-	m.CapabilityIDs[addressPath] = capabilityID
+	m.CapabilityIDs.Record(addressPath, capabilityID)
 
 	if reporter != nil {
 		reporter.MigratedLink(addressPath, capabilityID)
diff --git a/migrations/capcons/mapping.go b/migrations/capcons/mapping.go
new file mode 100644
index 0000000000..8eb1a45b38
--- /dev/null
+++ b/migrations/capcons/mapping.go
@@ -0,0 +1,52 @@
+/*
+ * Cadence - The resource-oriented smart contract programming language
+ *
+ * Copyright Dapper Labs, Inc.
+ *
+ * Licensed under the Apache License, Version 2.0 (the "License");
+ * you may not use this file except in compliance with the License.
+ * You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package capcons
+
+import (
+	"sync"
+
+	"github.com/onflow/cadence/runtime/interpreter"
+)
+
+type CapabilityIDMapping struct {
+	// CapabilityIDs' maps common.Address to map[interpreter.PathValue]interpreter.UInt64Value
+	capabilityIDs sync.Map
+}
+
+func (m *CapabilityIDMapping) Record(addressPath interpreter.AddressPath, capabilityID interpreter.UInt64Value) {
+	var accountCapabilityIDs map[interpreter.PathValue]interpreter.UInt64Value
+	rawAccountCapabilityIDs, ok := m.capabilityIDs.Load(addressPath.Address)
+	if ok {
+		accountCapabilityIDs = rawAccountCapabilityIDs.(map[interpreter.PathValue]interpreter.UInt64Value)
+	} else {
+		accountCapabilityIDs = map[interpreter.PathValue]interpreter.UInt64Value{}
+		m.capabilityIDs.Store(addressPath.Address, accountCapabilityIDs)
+	}
+	accountCapabilityIDs[addressPath.Path] = capabilityID
+}
+
+func (m *CapabilityIDMapping) Get(addressPath interpreter.AddressPath) (interpreter.UInt64Value, bool) {
+	rawAccountCapabilityIDs, ok := m.capabilityIDs.Load(addressPath.Address)
+	if !ok {
+		return 0, false
+	}
+	accountCapabilityIDs := rawAccountCapabilityIDs.(map[interpreter.PathValue]interpreter.UInt64Value)
+	capabilityID, ok := accountCapabilityIDs[addressPath.Path]
+	return capabilityID, ok
+}
diff --git a/migrations/capcons/migration_test.go b/migrations/capcons/migration_test.go
index c8ecb2cdf7..56b2f7dbb5 100644
--- a/migrations/capcons/migration_test.go
+++ b/migrations/capcons/migration_test.go
@@ -476,7 +476,7 @@ func testPathCapabilityValueMigration(
 
 	migration := migrations.NewStorageMigration(inter, storage)
 
-	capabilityIDs := map[interpreter.AddressPath]interpreter.UInt64Value{}
+	capabilityIDs := &CapabilityIDMapping{}
 
 	reporter := &testMigrationReporter{}
 
@@ -1325,7 +1325,7 @@ func testLinkMigration(
 
 	migration := migrations.NewStorageMigration(inter, storage)
 
-	capabilityIDs := map[interpreter.AddressPath]interpreter.UInt64Value{}
+	capabilityIDs := &CapabilityIDMapping{}
 
 	reporter := &testMigrationReporter{}